Now we examine in some detail the physics involved in nuclear weapons. First we take a look at the structure of an atom.
All matter is made up of atoms. Atoms consist of a small dense positively charged core called the nucleus which is surrounded by a cloud of negatively charged electrons. The nucleus is made up of electrically neutral particles called neutrons and positively charged particles called protons (see Figure 1). The number of protons in the nucleus is equal to the number of electrons, making the atom electrically neutral. For example, the nucleus of a hydrogen atom is made up of a single proton and has no neutrons. The oxygen nucleus (O-16) consists of eight protons and eight neutrons. The uranium nucleus (U-235) has 92 protons and 143 neutrons. Heavier atoms have a larger excess of neutrons over protons than lighter ones.
The protons and neutrons in nuclei are held together by strong nuclear forces which are stronger than any other force that acts between them, such as gravity. Surprisingly, the total mass of a nucleus is less than the total mass of the individual constituents (see Figure 1)! For example, the total mass of an oxygen nucleus is less than the total mass of eight protons and eight neutrons.
Figure 1 : The missing mass
The interaction between neutrons and protons in a nucleus is such that it effectively reduces, on the average, their mass, by a small fraction. Einstein’s theory of relativity explains that mass can be converted to energy, this energy being quantified by the famous formula, E = mc2 , for a mass m (c is the speed of light). Since the speed of light is extremely high (300,000km/second), even a very small amount of missing mass gets converted to a large amount of energy. This large amount of energy thus released is called the binding energy.
Let us compare this to another kind of binding energy involving atoms. Atoms tend to bind to each other to form molecules. For example, water is made up of molecules which contain two atoms of hydrogen and one of oxygen (see Figure 2).
Figure 2 : The water molecule H2O
The atoms in a molecule are held together by chemical bonds which form due to the way electrons distribute themselves in the molecule. The binding energy of a nucleus is about a million times more than this energy.
In chemical reactions, the atoms of the reacting molecules—but not their nuclei— rearrange themselves to form the product molecules. If the total amount of energy used by all the chemical bonds of the reactants is less than the amount used by the bonds in the products, then the excess energy is released in the form of heat and light. (This is what school textbooks call an exothermic reaction.)
Nuclear reactions involve a rearrangement of the neutrons and protons of the reacting nuclei to form the product nuclei. If the binding energy of the reactants is less than the binding energy of the products, then the excess energy is released in the form of radiation.
Because the binding energy of nuclei is about a million times more than the energy taken up by a chemical bond, the energy released in nuclear reactions is correspondingly about a million times more than what is released in chemical reactions.
Figure 3 : Binding energy per particle (nucleon) in a nucleus
As we saw earlier, energy will be released in a nuclear reaction if the total binding energy of the reactants is less than the binding energy of the products. Careful measurements of the binding energy of nuclei show that the binding energy per constituent particle (proton or neutron, collectively called nucleon) of a nucleus increases for light nuclei as their weight increases, where as for heavy nuclei it decreases as their weight increases (see Figure 4). For example, the binding energy per particle in deuterium (1 proton, 1 neutron) is less than in helium (2 protons, 2 neutrons).
However as the atom becomes heavier (exceeding about 26 protons in its nucleus, corresponding to the iron nucleus), the trend reverses. Hence, the binding energy per nucleon in uranium (92 protons, 143 neutrons) is less than in iron (26 protons, 30 neutrons).
There are therefore two possible kinds of nuclear reactions in which energy may be released. If a heavy nucleus splits into two roughly equal sized nuclei, energy will be released. Such a reaction is called a fission reaction. Heavy nuclei like uranium and Light Plutonium undergo fission. They split up into two roughly equal sized nuclei, accompanied by the emission of two to three neutrons and energy. Fission of these nuclei can occur spontaneously but can also be induced by the absorption of a neutron. These nuclei have such low binding energies that the kinetic energy of the incident neutron may be enough to split up the nucleus into smaller nuclei which are more stable and have higher binding energy.
Figure 4 : The fission process
If two light nuclei combine to form a single nucleus, then also there will be a release of energy. Indeed, such processes do occur and are called fusion reactions. These are the reactions that occur in the core of the sun and stars. An example of a fusion reaction that is used in nuclear weapons is one in which deuterium (1proton, 1 neutron) combines with tritium (1 proton, 2 neutrons) to give helium (2 protons,2 neutrons), accompanied by the release of a neutron and energy. In order for two light nuclei to fuse together they have to collide at very high speeds. Therefore the fusion fuel has to be heated to extremely high temperatures for the reaction to take place. Thus, most nuclear weapons which mainly rely on fusion reactions also have fission reactions taking place which trigger the subsequent fusion reaction.
As stated above (What are fission and fusion reactions?), the fission of nuclei like uranium and plutonium is accompanied by the emission of neutrons. We have already seen that heavier nuclei have a larger neutron excess than lighter ones. So, when a heavy nucleus fissions into two light nuclei, there will be some excess, "free" neutrons left over. Neutrons emitted by the fission of one nucleus can be absorbed by nearby ones, thus inducing them to split. This process will then proceed like an avalanche. The first nucleus to split will induce one or two nearby nuclei to split, each of which will induce one or two more to split, etc. These continually induced fissions form a chain reaction.
If all the neutrons emitted by the fission of nuclei (two or three in uranium and plutonium) were to induce fissioning of other nuclei, the process would multiply at a very fast rate. However, neutrons can be lost due to various reasons. They could escape from the material or they could be absorbed by the nuclei in various processes that do not result in fission. The number of neutrons available for fission, namely the number produced minus the number lost to other processes, determines whether the fission rate increases or decreases with time. The number of neutrons lost depends on the size of the assembly. It will be larger for smaller sizes since more neutrons will escape in smaller sized assemblies. It also depends on the density of fissile nuclei in the assembly—the higher the density, the more the chances of a neutron being captured by other nuclei and so the number of neutrons lost will be smaller. For the same reason, fewer neutrons will be lost with increasing purity of the material.
If, on the average, more neutrons are lost than produced, then the rate of fission would decrease with time and the whole process would die out. Such an assembly is said to be subcritical. If the number lost is exactly equal to the number produced, the assembly is critical. The chain reaction will then proceed at a constant rate. Finally, if the number produced exceeds the number lost, then the assembly is supercritical.
An idea of the amount of material required for an assembly to be critical is given by the critical mass, the mass of pure material for which this self-sustaining chain reaction occurs. A typical critical mass for a sphere of pure uranium could be anything from 16 to 52 kg, depending on the particular isotope considered.
In a nuclear reactor, the assembly is designed so that the criticality can be precisely controlled. It can be adjusted to be subcritical, critical or slightly supercritical.
A nuclear weapon is designed so that a subcritical assembly can suddenly be made supercritical. The critical mass of a fissile material decreases rapidly when the density of the material increases. A sub-critical assembly can be made critical or super-critical merely by compressing it, a process used in many weapons.